A physical system may be considered as a collection of individual constituents interacting with each other and their surroundings. The constituents, usually referred to as “agents”, may be characterized by several attributes and modes of interaction.
Systems may or may not be self-contained and such systems are usually referred to as being “closed” and “open” respectively. Furthermore, if the interactions between agents are sufficiently complicated, then the system is said to be “complex”. Moreover, if agents are endowed with a feedback mechanism for perceiving and reacting to signals and thus adjust their behaviour or interaction mechanisms, then they are said to be “adaptive”.
A system comprising many interacting agents is commonly referred to as a “multi-agent complex system”. One example of such a system is a pedestrian crowd.
A multi-agent complex system may be considered from two different points of view. Either one may consider the collective patterns that characterize the system in its entirety or one may focus on interaction mechanisms at the level of each individual constituent. These approaches are referred to as “macroscopic” and “microscopic” formulations respectively.
It is known to use a macroscopic model to describe a pedestrian crowd as a quasi-uniform medium, such as a fluid, without regard to individual constituents. It is typically low-resolution and results in only rough estimates of bulk measures, such as flows and densities, under certain conditions. Thus, it treats a pedestrian crowd as a quasi-uniform continuous fluid rather than interacting individuals.
Such a model is best suited to situations involving large spaces and large, uniform crowds, where there are no rapid variations in conditions, little change in the landscape and little variety in the purpose and function of the environment. Under these conditions, a macroscopic model may provide a reasonable estimate of the densities and flows.
An example of a macroscopic model is given in “Forecasting the Flow of People” by K. Ando, H. Ota and T. Oki, Railway Research Review, volume 45, page 8 (1988).
However, a macroscopic model is poorly suited to situations involving multi-directional flows and varied pedestrian profiles, where there are complicated geometries, rich in structure, and where there is a multitude of rapidly changing conditions. Under these conditions, macroscopic models may be misleading and lead to erroneous conclusions.
Despite this drawback, many methods of modelling pedestrian movement, including those used to set safety standards for buildings and spaces, use macroscopic approaches.
In contrast, microscopic models address the behavior of individual agents.
Microscopic models, such as Cellular Automata and other heuristic rule-based models, use ad-hoc parameterizations based on arbitrary probabilistic and statistical rules. These models are higher-resolution in that they consider individual agents and short-range variations in conditions. They also exhibit dynamic and emergent behavior. Nevertheless, they have several drawbacks. They tend to rely on having a homogeneous space and identical individuals. They are also difficult to calibrate and validate and are also erratic and unreliable. In fact, microscopic models which cannot be calibrated using empirically measured data are of questionable utility for practical applications and predictions. Thus, although qualitatively plausible, they are not suited to practical applications. At best they are used for illustrative purposes only.
Attempts have been made to formulate better microscopic models and an example is described in “Simulating dynamical features of escape panic” by Dirk Helbing, Illés Farakas and Tamás Vicsek, Nature, volume 407, pages 487 to 490 (2000). However, these models are applied to a specific set of circumstances which allow simplification.
It is desirable to develop a method of simulating movement of an autonomous entity through an environment for use in a method of modelling pedestrian crowd movement which can allow for design challenges such as non-uniform spaces, a variety of user profiles, a multitude of agent choices, dynamic changes in environment and chance events.
The method can be used for designing venues, troubleshooting flow problems, operational management, setting and implementing safety standards and quality control.